On the Use of a Supramolecular Coarse‐Grained Model for the Solvent in Simulations of the Folding Equilibrium of an Octa‐β‐peptide in MeOH and H2O

Molecular dynamics (MD) simulation can give a detailed picture of conformational equilibria of biomolecules, but it is only reliable if the force field used in the simulation is accurate, and the sampling of the conformational space accessible to the biomolecule shows many (un)folding transitions to allow for precise averages of observable quantities. Here, the use of coarse‐grained (CG) solvent MeOH and H₂O models to speed up the sampling of the conformational equilibria of an octa‐β‐peptide is investigated. This peptide is thought to predominantly adopt a 3₁₄‐helical fold when solvated in MeOH, and a hairpin fold when solvated in H₂O on the basis of the NMR data. Various factors such as the chirality of a residue, a force‐field modification for the solute, coarse‐graining of the solvent model, and an extension of the nonbonded interaction cut‐off radius are shown to influence the simulated conformational equilibria and the agreement with the experimental NMR data for the octa‐β‐peptide.     

Influence of variation of a side chain on the folding equilibrium of a β‐peptide: Limitations of one‐step perturbation

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94 , 597), the one‐step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔG_F,U of six hepta‐β‐peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔG_F,U values obtained using one‐step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft‐core atoms in the side chain of the fifth residue showed an overall accuracy of about k_BT for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference‐state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ₁ and χ₂ torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔG_F,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one‐step perturbation technique to compute free enthalpies of folding are discussed. © 2013 Wiley Periodicals, Inc.     

On the choice of a reference state for one‐step perturbation calculations between polar and nonpolar molecules in a polar environment

One‐step perturbation is an efficient method to estimate free energy differences in molecular dynamics (MD) simulations, but its accuracy depends critically on the choice of an appropriate, possibly unphysical, reference state that optimizes the sampling of the physical end states. In particular, the perturbation from a polar moiety to a nonpolar one and vice versa in a polar environment such as water poses a challenge which is of importance when estimating free energy differences that involve entropy changes and the hydrophobic effect. In this work, we systematically study the performance of the one‐step perturbation method in the calculation of the free enthalpy difference between a polar water solute and a nonpolar “water” solute molecule solvated in a box of 999 polar water molecules. Both these polar and nonpolar physical reference states fail to predict the free enthalpy difference as obtained by thermodynamic integration, but the result is worse using the nonpolar physical reference state, because both a properly sized cavity and a favorable orientation of the polar solute in a polar environment are rarely, if ever, sampled in a simulation of the nonpolar solute in such an environment. Use of nonphysical soft‐core reference states helps to sample properly sized cavities, and post‐MD simulation rotational and translational sampling of the solute to be perturbed leads to much improved free enthalpy estimates from one‐step perturbation. © 2012 Wiley Periodicals, Inc.     

Influence of Variation of a Side Chain on the Folding Equilibrium of a β‐Peptide

The ability to design well‐folding β‐peptides with a specific biological activity requires detailed insight into the relationship between the β‐amino acid sequence and the three‐dimensional structure of the peptide. Here, we present a molecular‐dynamics (MD) study of the influence of a variation of a side chain on the folding equilibrium of a β‐heptapeptide that folds into a 3₁₄‐helical structure. The side chain of the 5th residue, a valine, was changed into five differently branched side chains of different lengths and polarity, Ala, Leu, Ile, Ser, and Thr. Two computational techniques, long‐time MD simulations and the one‐step perturbation method, were used to obtain free enthalpies of folding. The simulations show that all six peptides exhibit similar folding behavior, and that their dominant fold is the same, i.e., a 3₁₄‐helix. Despite the similarities of their structural properties, a small stabilization effect of ca. 2 kJ mol^?1 on the folding equilibrium of the 3₁₄‐helical structure due to a branching C_γ‐atom in the β³‐side chain is observed. These results confirm those of previous circular dichroism (CD) studies. The length of side chain and its polarity seem to have no apparent (de)stabilization effect. Application of the cost‐effective one‐step perturbation method to predict free‐enthalpy differences appeared to yield an overall accuracy of about k_BT, which is not sufficient to detect the small stabilization effect.     

Establishing effective simulation protocols for β‐ and α/β‐peptides. III. Molecular mechanical model for acyclic β‐amino acids

All‐atom molecular mechanics (MM) force field parameters are developed for the backbone of acyclic β‐amino acid using an improved version of the multiobjective evolutionary algorithm (MOEA). The MM model is benchmarked using β³‐homo‐Alanine (β³‐hAla) diamide in water with SCC‐DFTB/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC‐DFTB/MM results regarding the distribution of key dihedral angles for the β³‐hAla diamide in water. The MM model is further applied to a β‐hepta‐peptide in methanol solution. The calculated NOE values and ³J coupling constants averaged over different trajectories are consistent with experimental data. By contrast, simulations using parameters directly transferred from the CHARMM22 force field for proteins lead to much worse agreement, which highlights the importance of careful parameterization for non‐natural peptides, for which the improved MOEA is particularly useful. Finally, as an initial application of the new force field parameters, the behaviors of a short random copolymer consisting of β amino acids in bulk solution and membrane/water interface are studied using a generalized Born implicit solvent model (GBSW). Results for four selected sequences show that segregation of hydrophobic and cationic groups occur easily at the membrane/solution interface for all sequences. The sequence that features alternating short blocks exhibits signs of lower stability at the interface compared to other sequences. These results confirm the hypothesis in recent experimental studies that β‐amino‐acid based random copolymers can develop a high degree of amphiphilicity without regular three‐dimensional structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Numerical Simulation of the Effect of Solvent Viscosity on the Motions of a β‐Peptide Heptamer

This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a β‐peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐(S,S)‐β³‐HAla(αMe)‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a β‐peptide on solvent viscosity has two regimes; a result that was observed in another computational study for α‐peptides.     

Determination of Solvatochromic Regression Coefficients for the Molybdenum(VI) Complex with Ethylenediamine‐N,N′‐diacetic Acid by Using Kamlet‐Abboud‐Taft Equation

The Solver, Microsoft Excel 2000 powerful optimization package, has been used to perform non‐linear least‐squares curve fitting on the basis of Gauss‐Newton method for the calculation of solvatochromic regression coefficients for the complexation of molybdenum(VI) with ethylenediamine‐N,N′‐diacetic acid and dissociation constants at 25°C and constant ionic strength 0.1 mol·L⁻¹ sodium perchlorate in different aqueous solutions of methanol. A combination of potentiometric and UV spectrophotometric methods have been used for experimental studies. Non specific and specific solute‐solvent interactions were interpreted by correlating the equilibrium data with solvent parameters using the Kamlet‐Abboud‐Taft solvatochromic equation. Finally the influence of the solvent on the stability of the complex was discussed on the basis of the correlation results and the contribution of α (hydrogen‐bond donor acidity), β (hydrogen‐bond acceptor basicity) and π* (dipolarity/polarizability) parameters.     

Molecular dynamics simulations and free energy calculations on the enzyme 4‐hydroxyphenylpyruvate dioxygenase

4‐Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one‐step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Theoretical investigation of solvent effects on tautomeric equilibrium of 2‐diazo‐4,6‐dinitrophenol

The density functional theory has been used to study the tautomeric equilibrium of 2‐diazo‐4,6‐dinitrophenol(DDNP) in the gas phase and in 14 solvents at the B3LYP/6‐31G* level. The solvent effects on the tautomeric equilibria were investigated by the self‐consistent reaction field theory (SCRF) based on conductor polarized continuum model (CPCM) in apolar and polar solvents and by the hybrid continuum‐discrete model in protic solvent, respectively. Solvent effects on the computed molecular properties, such as molecular geometries, dipole moments, E_LUMO, E_HOMO, total energies for DDNP tautomers and transition state, tautomerization energies and solvation energies have been found to be evident. The tautomeric equilibrium of DDNP is solvent‐dependent to a certain extent. The tautomer I (cyclic azoxy form) is preferred in the gas phase, while in nonpolar solvents tautomer I and II (quinold form) exist in comparable amounts, and in highly polar solvents, the tautomeric equilibrium is shifted in favor of the more polar tautomer II . © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Folding Dynamics of 10‐Residue β‐Hairpin Peptide Chignolin

Short peptides that fold into β‐hairpins are ideal model systems for investigating the mechanism of protein folding because their folding process shows dynamics typical of proteins. We performed folding, unfolding, and refolding molecular dynamics simulations (total of 2.7 μs) of the 10‐residue β‐hairpin peptide chignolin, which is the smallest β‐hairpin structure known to be stable in solution. Our results revealed the folding mechanism of chignolin, which comprises three steps. First, the folding begins with hydrophobic assembly. It brings the main chain together; subsequently, a nascent turn structure is formed. The second step is the conversion of the nascent turn into a tight turn structure along with interconversion of the hydrophobic packing and interstrand hydrogen bonds. Finally, the formation of the hydrogen‐bond network and the complete hydrophobic core as well as the arrangement of side‐chain–side‐chain interactions occur at approximately the same time. This three‐step mechanism appropriately interprets the folding process as involving a combination of previous inconsistent explanations of the folding mechanism of the β‐hairpin, that the first event of the folding is formation of hydrogen bonds and the second is that of the hydrophobic core, or vice versa.     

Folding–Unfolding Equilibrium of a Methylidene‐Substituted β‐Peptide

β‐Peptides possess the ability to fold into secondary structure elements, and this property, together with resistance to biodegradation, makes these compounds interesting for pharmaceutical applications. Recently, a novel class of β‐peptides containing methylidene moieties was described. The GROMOS 53A6 force field was used to simulate the folding equilibrium of a β³‐hexapeptide with methylidene (CH₂?) groups at all six CA‐atoms. Due to the rotational barriers induced by these methylidene groups, the helical secondary‐structure elements, normally found in β³‐peptides, are disfavored in this molecule. Simulations, started from fully extended and 3₁₄‐helical conformations, showed that the molecule adopts a complete 2₈‐helix for ca. 5% of the time and partial 2₈‐helical conformations for ca. 20% of the time. Yet, as suggested by experiments, the folding equilibrium is dominated by unfolded conformations.     

Simply enhancing throughput of free‐flow electrophoresis via organic‐aqueous environment for purification of weak polarity solute of phenazine‐1‐carboxylic acid in fermentation of Pseudomonas sp. M18

Herein, a simple novel free‐flow electrophoresis (FFE) method was developed via introduction of organic solvent into the electrolyte system, increasing the solute solubility and throughput of the sample. As a proof of concept, phenazine‐1‐carboxylic acid (PCA) from Pseudomonas sp. M18 was selected as a model solute for the demonstration on feasibility of novel FFE method on account of its faint solubility in aqueous circumstance. In the developed method, the organic solvent was added into not only the sample buffer to improve the solubility of the solute, but also the background buffer to construct a uniform aqueous‐organic circumstance. These factors of organic solvent percentage and types as well as pH value of background buffer were investigated for the purification of PCA in the FFE device via CE. The experiments revealed that the percentage and the types of organic solvent exerted major influence on the purification of PCA. Under the optimized conditions (30 mM phosphate buffer in 60:40 (v/v) water‐methanol at an apparent pH 7.0, 3.26 mL/min background flux, 10‐min residence time of injected sample, and 400 V), PCA could be continuously purified from its impurities. The flux of sample injection was 10.05 μL/min, and the recovery was up to 93.7%. An 11.9‐fold improvement of throughput was found with a carrier buffer containing 40% (v/v) methanol, compared with the pure aqueous phase. The developed procedure is of evident significance for the purification of weak polarity solute via FFE.     

Atomistic insight into chondroitin‐6‐sulfate glycosaminoglycan chain through quantum mechanics calculations and molecular dynamics simulation

Chondroitin‐6‐sulfate (C6S) is a glycosaminoglycan (GAG) constituent in the extracellular matrix, which participates actively in crucial biological processes, as well as in various pathological conditions, such as atherosclerosis and cancer. Molecular interactions involving the C6S chain are therefore of considerable interest. A computational model for atomistic simulation was built. This work describes the design and validation of a force field for a C6S dodecasaccharide chain. The results of an extensive molecular dynamics simulation performed with the new force field provide a novel insight into the structure and dynamics of the C6S chain. The intramolecular H‐bonds in the disaccharide linkage region are suggested to play a major role in determining the chain structural dynamics. Moreover, the unravelling of an additional H‐bond involving the sulfate groups in C6S is interesting as changes in sulfation have been claimed to be an important factor in several diseases. The force field will prove useful for future studies of crucial interactions between C6S and various nanoassemblies. It can also be used as a basis for modeling of other GAGs. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A Hybrid statistical mechanics—quantum chemical model for proton transfer in 5‐azauracil and 6‐azauracil in water solution

A hybrid statistical physics—quantum‐chemical methodology was implemented to study the water‐assisted intramolecular proton‐transfer processes in 5‐ and 6‐azauracils in aqueous solutions. The solvent effects were included in the model by explicit inclusion of two pairs of water molecules, which model the relevant part of the first hydration shell around the solute. The position of these water molecules was initially estimated by carrying out a classical Metropolis of dilute water solutions of the title compounds and subsequently analyzing solute–solvent intermolecular interactions in the Monte Carlo‐generated configurations. Sequentially to the statistical physics simulation, ab initio quantum mechanical (QM) level of theory was implemented. The effects of the water as solvent (at ab initio QM level) were introduced at two different levels—using solute–solvent clusters (four‐water molecules) and using the same clusters embedded in an external continuum. Full geometry optimizations of these complexes were carried out at MP2/6–31 + G(d, p) and conductor‐polarizable continuum model (C‐PCM)/MP2/6–31 + G(d, p). Single point calculations were performed at CCSD(T)/6–31 + G(d, p)//MP2/6–31 + G(d, p) computational level to obtain more accurate energies. According to our calculations hydrated azauracils should exist in three forms: mainly dioxo form and two hydroxy forms. The calculated proton transfer activation energies for tautomeric reactions of 5‐azauracil and 6‐azauracil show different pictures for these two compounds. According to C‐PCM/MP2/6–31 +G(d, p) data, water‐assisted proton transfer in 5‐azauracil realizes through two parallel reactions: 1,3,5‐triazine‐2,4(1H,3H)‐dione → 6‐hydroxy‐1,3,5‐triazin‐2(1H)‐one and 1,3,5‐triazine‐2,4(1H,3H)‐dione → 4‐hydroxy‐1,3,5‐triazin‐2(1H)‐one. Tautomeric equilibrium in 6‐azauracil in water could occur by two contiguous reactions: 1,2,4‐triazine‐3,5(2H,4H)‐dione → 5‐hydroxy‐1,2,4‐triazin‐3(2H)‐one and 5‐hydroxy‐1,2,4‐triazin‐3(2H)‐one → 3‐hydroxy‐1,2,4‐triazin‐5(2H)‐one. The proton transfer investigated reactions in 5‐ and 6‐azauracils involve concerted atomic movement. © 2015 Wiley Periodicals, Inc.     

Improved treatment of cyclic β‐amino acids and successful prediction of β‐peptide secondary structure using a modified force field: AMBER*C

We added parameters to the AMBER* force field to model cyclic β‐amino acid derivatives more accurately within the commonly used MacroModel program. In an effort to generate an improved treatment of cyclohexane and cyclopentane conformational preferences, carbon–carbon torsional parameters were modified and incorporated into a force field we call AMBER*C. Simulation of trans‐2‐aminocyclohexanecarboxylic acid (trans‐ACHC) and trans‐2‐aminocyclopentanecarboxylic acid (trans‐ACPC) derivatives using AMBER*C produces more realistic energy differences between (pseudo)diaxial and (pseudo)diequatorial conformations than does simulation using AMBER*. AMBER*C molecular dynamics simulations more accurately reproduce the experimental hydrogen‐bonding tendencies of simple diamide derivatives of trans‐ACHC and trans‐ACPC than do simulations using the AMBER* force field. More importantly, this modified force field allows accurate qualitative prediction of the helical secondary structures adopted by β‐amino acid homo‐oligomers. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 763–773, 2000     

An interaction potential to study the thermal structure evolution of a thermoelectric material: β‐Cu2Se

An interaction potential model has been developed, for the first time, for β‐Cu₂Se using the ab initio derived data. The structure and elastic constants of β‐Cu₂Se using the derived force‐field are within a few percent of DFT derived structure and elastic constants and reported experimental structure. The derived force‐field also shows remarkable ability to reproduce temperature dependent behavior of the specific heat and thermal expansion coefficient. The thermal structure evolution of the β‐Cu₂Se is studied by performing the molecular dynamic simulations using the derived force‐field. The simulation results demonstrate that the Cu ions moves around the equilibrium lattice position within the temperature range of 500–800 K. However, at a temperature > 800 K, the Cu ions starts diffusing within the material, while the Se ions remains in their lattice position. The evaluated thermodynamic properties such as free energy and excess entropy, show that the increased Cu–Se interaction with the temperature makes the system more thermodynamically stable. © 2017 Wiley Periodicals, Inc.     

Rapid sampling of all‐atom peptides using a library‐based polymer‐growth approach

We adapted existing polymer growth strategies for equilibrium sampling of peptides described by modern atomistic forcefields with a simple uniform dielectric solvent. The main novel feature of our approach is the use of precalculated statistical libraries of molecular fragments. A molecule is sampled by combining fragment configurations—of single residues in this study—which are stored in the libraries. Ensembles generated from the independent libraries are reweighted to conform with the Boltzmann‐factor distribution of the forcefield describing the full molecule. In this way, high‐quality equilibrium sampling of small peptides (4–8 residues) typically requires less than one hour of single‐processor wallclock time and can be significantly faster than Langevin simulations. Furthermore, approximate, clash‐free ensembles can be generated for larger peptides (up to 32 residues in this study) in less than a minute of single‐processor computing. We discuss possible applications of our growth procedure to free energy calculation, fragment assembly protein‐structure prediction protocols, and to “multi‐resolution” sampling. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011